A007984 Number of essential graphs with n nodes (in 1-1 correspondence with Markov equivalence classes of acyclic digraphs).

1, 2, 11, 185, 8782, 1067825, 312510571, 212133402500, 326266056291213, 1118902054495975181, 8455790399687227104576, 139537050182278289405732939, 4991058955493997577840793161279

Offset

1,2

References

S. B. Gillispie and M. D. Perlman, Enumerating Markov equivalence classes of acyclic digraph models, Proc. of Conf. on Uncertainty in Artificial Intelligence (2001), 171-177.

S. B. Gillispie and M. D. Perlman, The size distribution for Markov equivalence classes of acyclic digraph models, Artificial Intelligence, 141 (2002), 137-155.

Bertran Steinsky, Enumeration of Labelled Essential Graphs, Ars Comb., 111, (2013), 485-494

Links

Table of n, a(n) for n=1..13.

S. B. Gillispie and M. D. Perlman, Enumerating Markov equivalence classes of acyclic digraph models, Univ. of Washington, Dept. of Statistics, Technical Reports.

S. B. Gillispie and M. D. Perlman, The size distribution for Markov equivalence classes of acyclic digraph models, Univ. of Washington, Dept. of Statistics, Technical Reports.

Crossrefs

Cf. A368569 (refined by # arcs).

Sequence in context: A124836 A365361 A013104 * A132871 A140314 A226052

Adjacent sequences: A007981 A007982 A007983 * A007985 A007986 A007987

Keyword

nonn

Author

David Madigan (madigan(AT)stat.washington.edu)

Extensions

More terms from Steven B. Gillispie (gillisp(AT)u.washington.edu), Oct 21 2003

a(10) corrected by Steven B. Gillispie (gillisp(AT)u.washington.edu), Aug 14 2007, who says: I have learned from Bertran Steinsky (who determined the correct number) that there was an error in my computer software that computed a(10). The correct value is 1118902054495975181.

a(11)-a(13) from Bertran Steinsky, Jun 24 2013

Status

approved